Electric and magnetic fields: field concepts, Coulomb and Lorentz force, motion of charged particles, induction
What this domain tests
Electric and magnetic fields covers the field concept, Coulomb's law, the motion of charged particles in E and B fields, and electromagnetic induction. Typical tasks describe a cathode-ray tube, a mass spectrometer or a transformer and ask for field strengths, trajectories, induced voltages and a justified statement about direction.
Electric field
- Field strength E = F/q, unit V/m = N/C; field lines run from + to − and never cross.
- Coulomb: F = (1/4πε₀)·q₁q₂/r² with 1/4πε₀ = 8.99·10⁹ N m²/C².
- Uniform field of a parallel-plate capacitor: E = U/d; potential φ, voltage U = Δφ, energy qU.
- Acceleration in the field: qU = ½mv².
Magnetic field
- Force on a moving charge F = qvB·sin α; direction from the right-hand rule for positive charges, the left hand for electrons.
- F is always perpendicular to v, so it does no work and the speed stays constant - the path is a circle with r = mv/(qB).
- A velocity selector balances qE = qvB, giving v = E/B.
Induction
- Magnetic flux Φ = B·A·cos α; induced voltage U_ind = −N·dΦ/dt.
- Lenz's law: the induced current opposes the change that causes it, and this fixes the sign.
- Applications: generator, transformer (U₁/U₂ = N₁/N₂), eddy currents, self-induction.
Worked example
An electron is accelerated through U = 200 V and enters B = 5.0 mT perpendicular to its velocity. Speed: v = √(2eU/m) = √(2·1.60·10⁻¹⁹·200 / 9.11·10⁻³¹) ≈ 8.4·10⁶ m/s. Radius: r = mv/(eB) = (9.11·10⁻³¹ · 8.4·10⁶) / (1.60·10⁻¹⁹ · 5.0·10⁻³) ≈ 9.6·10⁻³ m, about 9.6 mm. The magnetic field changes only the direction, so the speed gained in the electric field is used unchanged - say this explicitly.
Traps
- Using the right-hand rule for an electron without reversing the result.
- Claiming a magnetic field accelerates a charge along its direction of motion.
- Forgetting that induction needs a changing flux - a static field through a static loop gives zero.
- Mixing up U and E in the plate capacitor, or using the plate separation as the path length in a deflection problem.